Fenil's Library

You don’t need to be a mathematician to be able to be a good investor. In fact, all it takes is fifth standard mathematics, something most of us tend to forget.

We attempt here a recall of the basic math one ought to know, especially in an environment like this, when the chips are down across sectors. 

A 50% loss can wipe out a 100% gain 

Let us say you bought some stock at Rs 500 per share. The stock did well and went up to a peak price of Rs 1,000. What was the gain? The gain was Rs 500 (Rs 1000 - Rs 500) or 100% in percentage terms ((Rs 500/Rs 500) x 100%)). 

Now, say the stock started to fall after reaching the peak and its price came back to Rs 500. Your loss is Rs 500 (Rs 1,000 - Rs 500) or 50% ((Rs 500/Rs 1000) x 100%).

So a 50% loss has wiped out a 100% gain. In other words, you now have to make a 100% gain to be back at the peak level again.

Or take the Bombay Stock Exchange Sensex, which has fallen to around 11,000 from the high of 21,000 reached in January last year. The 10,000-point fall from the peak translates to a loss of 48% ((10,000/21,000) x 100%).

But how much does the Sensex need to gain from here to be back at 21000? It needs to gain 10,000 points or 91% ((10,000/11,000) x 100). 

Now that’s simple, isn’t it?

However, many of us simply don’t get it and even seasoned guys sometimes err in treating percentages no differently from numbers.

The lack of understanding even shows in newspaper columns.

For example, Jerry Rao —- alumnus of IIM Ahmedabad, founder of IT firm Mphasis Corporation, which merged with BFL Software in 2000 to form Mphasis-BFL, and former consumer banking head of Citibank in India, no less —- wrote in a leading newspaper on October 6, 2008: “If stock market wealth drops by 50% in six months, we get concerned. We conveniently forget that it went up by 200% over the previous two years. At the end of 30 months, we are still 150% ahead.” 

Now, a fifth-grader would know that at the end of those 30 months, we are not 150% ahead but 50% ahead.

Say you invest Rs 100 today. A 200% gain on this would mean your investment has grown to Rs 300 (Rs 100 + 200% of Rs 100). A 50% fall from Rs 300 would mean your investment is worth Rs 150 (Rs 300 - 50% of Rs 300), which would mean you are ahead by 50% (((Rs 150 - Rs 100)/Rs 100) x 100%) and not 150% as Rao wrote. 

A 20% salary cut wipes of a 25% increment 

In a somewhat similar vein, let us now take the salary cuts being handed out by employers everywhere. 

Say during the course of last year, an individual got an increment of 25% and his salary increased from Rs 4 lakh to Rs 5 lakh (Rs 4 lakh + 25% of Rs 4 lakh). Now, if his company cuts his salary by 20%, his salary will go down by Rs 1 lakh (20% of Rs 5 lakh) and be back at Rs 4 lakh.

So, a 20% salary cut will wipe out a 25% increment. 

In other words, you would now need a 25% increment to be back at the level you were in. 

Would you still let the HR guys get away saying you are left with a 5% gain?

Let us say an organisation decides to cut salaries of people who earn above Rs 5 lakh by 10% and spare those earning Rs 5 lakh or below.

This means, an individual who earns a salary of Rs 5 lakh does not take any cut. But anyone who earns even Re 1 over Rs 5 lakh takes a salary cut of 10%, i.e. Rs 50,000 (10% of Rs 5,00,001). 

In other words, that one rupee more has cost you Rs 50,000. Chances are you would now be 

getting what your junior gets.

That is why salary cuts need to be graded, and not direct as in the example above. In the example above, it would have been fair that the employer effected a cut only on the extra rupee one earned over Rs 5 lakh rather than on the whole sum. 

Falling inflation need not mean falling prices 

The inflation number declared by the government every week has been falling for sometime now and is almost near zero percent. However, there is no sign of prices going down anywhere. 

Now why aren’t prices falling? For this, we must first understand what inflation is. Inflation is the rate of increase in price. If the price a product increases from Rs 10 to Rs 12, we say inflation is 20% ((Rs 2/Rs 10) x 100%). Let us say the next month the cost of the product goes up to Rs 13. What is the inflation now? The inflation is 8.33% ((Re 1/ Rs 12) x 100%). Now, inflation has fallen from 20% to around 8.33%. But has the price fallen? No. What has fallen is the rate of increase in price, not the price. 

Overall prices will fall when inflation turns negative. Even then, you and I may not see falling prices because the prices of the basket of goods and services that we buy may not fall at all, or worse, continue to rise.